Normal Heights Homes for Sale â Normal Heights Real Estate in San Diego CA Normal Heights was named after the State Normal School which later became San Diego State University. Centrally located with I-805, I-8 and I-15 as its western, northern and eastern borders, transportation in and out of the area is convenient. With the year-round warm weather, Normal Heights homes for sale has so much to offer with the San Diego Zoo and SeaWorld just minutes away. Viewnormalheightshomes.com~Site InfoWhoisTrace RouteRBL Check